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A twohinged semicircular arch of radius 'R' carries a concentrated load 'W' at the crown.
The horizontal thrust is
The horizontal thrust is
- a)W/2π
- b)W/π
- c)2W/3π
- d)4W/3π
Correct answer is option 'B'. Can you explain this answer?
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A twohinged semicircular arch of radius 'R' carries a concentrated loa...
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Explanation:
To find the horizontal thrust of the two-hinged semicircular arch, we can use the principle of statics. The horizontal thrust is the force exerted by the arch on its supports in the horizontal direction.
Steps to find the horizontal thrust:
1. Draw the free body diagram of the arch and identify the forces acting on it.
2. Apply the equations of equilibrium to solve for the horizontal thrust.
Free Body Diagram:
Considering the arch in equilibrium, the following forces act on it:
- The concentrated load W at the crown
- The horizontal thrust H at the supports
- The vertical reaction forces V1 and V2 at the supports
Equilibrium Equations:
Applying the equations of equilibrium in the horizontal and vertical directions:
- Horizontal equilibrium: ∑Fx = 0
- Vertical equilibrium: ∑Fy = 0
Horizontal Equilibrium:
Since there are no horizontal external forces, the horizontal thrust H is the only force acting in the horizontal direction.
∑Fx = H = 0
Vertical Equilibrium:
Considering the forces in the vertical direction:
∑Fy = V1 + V2 - W = 0
Since the arch is in equilibrium, the vertical reaction forces V1 and V2 must balance the load W.
Resultant Horizontal Thrust:
From the equation of horizontal equilibrium, we know that H = 0. Therefore, the horizontal thrust is zero.
Therefore, the correct option is (b) H = 0, which means the horizontal thrust is zero.
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A twohinged semicircular arch of radius 'R' carries a concentrated load 'W' at the crown.The horizontal thrust isa)W/2πb)W/πc)2W/3πd)4W/3πCorrect answer is option 'B'. Can you explain this answer?
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